Interactive systems and their human being-machine-interfaces are known for the human being-computer-interaction, wherein the human being-machine-interfaces are provided with a device for the automatic recognition of non-tactile or tactile gestures performed by human beings. The gesture can principally be derived from every posture and every movement of the body, wherein hand gestures have most importance. The gesture recognition device is provided with a device for the optical acquisition in particular of the gesticulating hand, wherein the image information generated thereby is processed with corresponding algorithms in order to derive a gesture out of the image information. The device for the optical acquisition of a non-tactile gesture is conventionally a camera that disadvantageously takes a large space and involves high investment costs. Camera-based devices for the gesture recognition in miniaturized design with low costs, which would be for example advantageous for the use in mobile phones, are therefore not to be realized. Furthermore, camera-based devices have disadvantageously a high energy consumption, whereby mobile applications can only be realized with difficulty. High-speed spectrometers are alternatively known, which cannot provide remedy with respect to the miniaturized design with low costs. Touch screens in particular for mobile telephones are furthermore known, however the touch screens are suitable only for the recognition of tactile gestures and not for the recognition of non-tactile gestures.